潛在構念發展歷程的成長模式與估計策略：二階潛在成長模式模型設定與估計方法的模擬與實徵分析研究

The key of human developmental research is to capture the "change" over time. Through multiple waves of repeated measures, growth trajectory can be estimated via growth modeling. If the research topic involves abstract psychological constructs—such as the cognitive development of kids as one of the focused of KIT dataset (Kids in Taiwan: National Longitudinal Study of Child Development & Care), the second-order latent growth modeling (SLGM) has to be adapted. The observed variable in measurement model must be scaled appropriately with longitudinal invariance across time; otherwise, the parameter estimation of trajectory will be biased and invalid. The lack of clear recommendations in the literature regarding the scaling and model specification. Given the complexity of SLGM modeling and parameters involved, and the missing data associated with longitudinal datasets, the model setting for SLGM warrants in-depth exploration. This two-years research consist of three studies, involving Monte Carlo simulations and empirical data analysis from KIT, by exploring the impact of different scaling methods and model settings on parameter bias and estimation performance. Efficacy of parameter estimation of SLGM on the longitudinal data with missing structures also examined. The Monte Caro simulation study found that the invariance characteristics of the data are the primary factors determining SLGM model settings. Missing data, under conditions of random missingness and sufficient sample size, had minimal impact on SLGM parameter estimation. Under different simulated conditions and model setting strategies, the performance of marker variable coding and effect coding was relatively similar. However, effect coding has advantages such as model simplification, lower standard errors, and higher statistical power. Moreover, it performed better in terms of longitudinal invariance condition. In contrast, marker variable coding requires careful consideration of the choice of marker variables and a preliminary examination of longitudinal invariance in advance, as failure to do so could result in significant fluctuations in SLGM estimation. In the empirical analysis of cognitive development data from KIT dataset, varying degrees of measurement non-invariance were observed, leading to inconsistent results. Conversely, effect coding produced stable results, but it required parameter constraints in the measurement model, which limits its applicability to Bayesian estimation using MCMC algorithms in Mplus. This research discusses statistical analysis of developmental trajectory growth, addressing the deficiencies in current statistical technical guidelines and the gaps in related theoretical knowledge. It provides a reference for empirical data analysis while also leaving many research topics that require further exploration, such as the influence of broader sample sizes on various SLGM models and extending from linear to nonlinear models. Further research in these areas is essential to establish a more comprehensive methodological knowledge and technical guidelines.